Method for Characterization of Limit Cycles in Power Systems

Limiters are normally used to prevent damage in power system equipment. In the literature, it is recognized that limiters can also contribute to stability of nonlinear power system models, preventing large excursion of variables in case of large disturbances. This paper presents a case where the generator field voltage is bounded by the action of an Automatic Voltage Regulator (AVR) limiter, giving rise to a stable and non-smooth limit cycle. A method characterizing non-smooth switching-induced limit cycles is applied. This procedure requires the formulation of the AVR model as a hybrid dynamical system. The applied methodology consists of an extension of the shooting method in time-domain to hybrid dynamical systems. It resorts to the composition property of the fundamental matrix that allows the insertion of a proper saltation matrix just when a discontinuous event occurs in the evolution of the power system trajectory. So doing, it is possible to compute the power system monodromy matrix in case of non-smooth switching-induced limit cycles.